What is the derivative of xarctan(2x-1/4 ln(1+4x^2)) ?

The derivative of xarctan(2x-1/4 ln(1+4x^2)) is arctan(2x)

What is the first derivative of xarctan(2x-1/4 ln(1+4x^2)) ?

The first derivative of xarctan(2x-1/4 ln(1+4x^2)) is arctan(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x arctan (2 x) - \frac{1}{4} ln (1 + 4 x^{2}))

arctan (2 x)

Solution steps

\frac{d}{d x} (x arctan (2 x) - \frac{1}{4} ln (1 + 4 x^{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x arctan (2 x)) - \frac{d}{d x} (\frac{1}{4} ln (1 + 4 x^{2}))

\frac{d}{d x} (x arctan (2 x)) = arctan (2 x) + \frac{2 x}{4 x ^{2} + 1}

\frac{d}{d x} (\frac{1}{4} ln (1 + 4 x^{2})) = \frac{2 x}{1 + 4 x ^{2}}

= arctan (2 x) + \frac{2 x}{4 x ^{2} + 1} - \frac{2 x}{1 + 4 x ^{2}}

Simplify

arctan (2 x) + \frac{2 x}{4 x ^{2} + 1} - \frac{2 x}{1 + 4 x ^{2}} : arctan (2 x)

= arctan (2 x)

What is the derivative of xarctan(2x-1/4 ln(1+4x^2)) ?
The derivative of xarctan(2x-1/4 ln(1+4x^2)) is arctan(2x)
What is the first derivative of xarctan(2x-1/4 ln(1+4x^2)) ?
The first derivative of xarctan(2x-1/4 ln(1+4x^2)) is arctan(2x)